Which of the following is an equation of the line that is tangent to f(x)=-x^2+3x+9 at the point (-1,5)?
To find the equation of the line tangent to a curve at a given point, we need to find the slope of the curve at that point and use it to write the equation of the tangent line in point-slope form.
To find the slope of the curve at (-1, 5), we need to find the derivative of f(x)=-x^2+3x+9 and evaluate it at x=-1:
f'(x)=-2x+3
f'(-1)=-2(-1)+3=5
So the slope of the curve at (-1, 5) is 5.
Now we can use point-slope form to write the equation of the tangent line:
y - 5 = 5(x + 1)
Simplifying this equation, we get:
y = 5x + 10
So the equation of the line tangent to f(x)=-x^2+3x+9 at the point (-1,5) is y = 5x + 10.